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  • 1.
    Asami-Johansson, Yukiko
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Attorps, Iris
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Laine, Anu
    University of Helsinki, Helsinki, Finland.
    Comparing the practices of primary school mathematics teacher education Case studies from Japan, Finland and Sweden2017In: PROCEEDINGS OF THE TENTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION (CERME10) / [ed] Dooley, T.; Gueudet, G., Dublin, 2017, p. 1602-1609Conference paper (Refereed)
    Abstract [en]

    In this study, we have observed three different teacher educators’ lessons, concerning area determination of polygons in primary school teacher training courses in Japan, Finland and Sweden. The aim of this paper is to investigate the main elements of the lessons and to compare the differences between the countries. We focus on how the teacher educators relate the didactic construction of the lessons for prospective teachers to the school mathematical and didactical organisations by applying Chevallard’s anthropological theory of the didactic (ATD). The analysis shows how the curricula and the different traditions of teaching practice in each country influence the mathematical and didactical construction of the lessons.

  • 2.
    Asami-Johansson, Yukiko
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Science Education, University of Copenhagen, Copenhagen, Denmark.
    Attorps, Iris
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Winsløw, C.
    Department of Science Education, University of Copenhagen, Copenhagen, Denmark.
    Comparing mathematics education lessons for primary school teachers: case studies from Japan, Finland and Sweden2019In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to investigate and compare lessons given in primary school teacher education in Japan, Finland and Sweden. We analyse one lesson from each country and compare them using a common framework. Chevallard’s anthropological theory of the didactic (ATD) is used to frame this analysis and in particular to model teacher educators' didactic organization of the lessons. The focus is on how the didactic organizations of the teacher educators relate to the mathematical and didactic organizations of primary school. Based on official documents and viewpoints of the teacher educators, we also discuss how the contents and descriptions of the national curricula, and the different traditions of the teaching practices in each country, influence the didactic organizations found in the lessons. 

  • 3.
    Backman, Mathilda
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Se mig!: En studie om matematiskt särskilt begåvade elever2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien är att utforska vilka uppfattningar lågstadielärare har av matematiskt särskilt begåvade elever, samt undersöka vilka arbetssätt lärare har för att motivera och stimulera de här eleverna i matematik. Studien har en metod med kvalitativ ansats med en fenomenografisk och fenomenologisk inriktning. Datainsamlingsmetoden för studien är intervjuer. Fyra lärare intervjuades och de är alla något så när överens om att matematiskt särskilt begåvade elever skiljer sig från andra elever, samt på vilket sätt de gör det. Lärarnas uppfattningar av matematiskt särskilt begåvade elever överensstämmer även med tidigare forskning gällande ämnesområdet. Samtliga lärares arbetssätt innehåller extra anpassningar för de här eleverna och största skillnaden som kunnat urskiljas mellan arbetssätten är huruvida de även innehåller särskilt stöd. Till viss del överensstämmer dessa uppfattningar även med tidigare forskning då det även där råder oenigheter om matematiskt särskilt begåvade elever ska differentieras eller inte.

  • 4.
    Berglund, Jessica
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Vill du spela bingo med mig?: En studie med laborativt material för att utveckla elevers kunskaper om positionssystemet2019Independent thesis Advanced level (degree of Master (Two Years)), 240 HE creditsStudent thesis
    Abstract [sv]

    Studiens syfte är att med hjälp av en learning study med förtest och eftertest undersöka elevers förkunskaper om positionssystemet samt om elever genom laborativt material kan fördjupa sina kunskaper om positionssystemet. Studiens teoretiska utgångspunkt är hämtad från variationsteorin. Att arbeta med ett laborativt material möjliggör för eleverna att utveckla en utökad förståelse för positionssystemet med basen 10. En av slutsatserna från denna studie är att ett variationsteoretiskt perspektiv på undervisningen underlättar lärandet.

  • 5.
    Blank, Jonathan
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Motivation till matematik: En kvalitativ studie om hur elever i årskurs 4–6 kan motiveras i matematikundervisningen ur ett lärarperspektiv2019Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna studie är att undersöka hur lärare arbetar med att motivera elever i årskurs 4–6 i matematik. För att undersöka detta genomfördes klassrumsobservationer och semistrukturerade intervjuer med tre verksamma lärare i årskurs 4–6. Studiens resultat visar att en hög motivation hos eleverna skapas av tydliga strukturer i klassrummet, att läraren synliggör målen för eleverna, att läraren varierar sina arbetssätt och undervisningsformer samt att eleven tar ansvar för sitt eget lärande. 

  • 6.
    Khulbe, Manisha
    et al.
    Ambedkar Institute of Advanced Communication Technologies and Research (AIACTR), Delhi, India.
    Tripathy, Malay Ranjan
    Amity School of Engineerng and Technology, Amity University, Noida, India.
    Parthasarathy, Harish
    Netaji Subhash Institute of Technology (NSIT), N. Delhi, India.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Lagovsky, Boris
    Russian Technological University, MIREA, Moscow, Russia.
    Inverse Scattering and Imaging Using Second Order Optical Nonlinearities2019In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, IEEE, 2019, p. 1086-1089Conference paper (Refereed)
    Abstract [en]

    In this paper a mathematical technique is developed to find the parameters of a medium in terms of its scattered electromagnetic fields. Optical nonlinearity plays an important role in finding the scattering parameters of a medium. Using perturbation theory and nonlinear inverse scattering techniques with first order, second order and third order optical nonlinearity we find scattered electromagnetic fields. Using error minimization techniques parameters are estimated in term of permittivity and permeability up to second order. © 2019 IEEE.

  • 7.
    Lagovsky, B. A.
    et al.
    Russian Technological University (MIREA), Moscow, Russia.
    Samokhin, A. B.
    Russian Technological University (MIREA), Moscow, Russia.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Regression Methods of Obtaining Angular Superresolution2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738539Conference paper (Refereed)
    Abstract [en]

    New methods of signal processing based on nonlinear regression methods are presented. They allow us to restore images of individual objects of group targets with superresolution at signal-to-noise ratios that are significantly lower than those provided by the known methods.

  • 8.
    Nardi, Elena
    et al.
    School of Education and Lifelong Learning, University of East Anglia, Norwich, UK.
    Ryve, Andreas
    School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Stadler, Erika
    Department of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.
    Viirman, Olov
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Mathematics, Karlstad University, Karlstad, Sweden.
    Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus2014In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 16, no 2, p. 182-198Article in journal (Refereed)
    Abstract [en]

    In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards 'scaling-up' the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as "legitimate peripheral participation" from the theory of Communities of Practice and "didactic contract" from the Theory of Didactic Situations. 

  • 9.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    On a Method of Solution to Dispersion Equations in Electromagnetics2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli, 2019, article id 8738297Conference paper (Refereed)
    Abstract [en]

    A possible general approach to the analysis of dispersion equations (DEs) of electromagnetics is presented. The method takes into account the known explicit forms of DEs describing eigenoscillations and normal waves in layered structures and is based on the development of the notion of generalized cylindrical polynomials. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the DE roots and validate iterative numerical solution techniques.

  • 10.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Trigonometric and cylindrical polynomials and their applications in electromagnetics2019In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed)
    Abstract [en]

    Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

  • 11.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Kuzmina, Ekaterina
    Moscow Technological University MIREA, Moscow, Russia.
    On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides2018In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper (Refereed)
    Abstract [en]

    Theory of complex waves (see e.g. [1] and references therein) accumulated a big volume of results. However, its biggest drawback remains which brakes significantly the development of the theory: absence of rigorous proofs of the existence of complex waves. In this respect, studies of complex waves in open metal-dielectric waveguides has been essentially enhanced when two new families of symmetric (angle-independent) complex waves have been identified [2, 3] in a dielectric rod (DR) and Goubau line (GL) with homogeneous dielectric cover: surface complex waves occurring as perturbations of real surface waves caused by the presence of lossy dielectric, and pure complex waves which have no counterpart in the set of real waves. Existence of the latter family of complex waves has been shown using a special technique and the proof [3] of the existence of an infinite set of complex roots of the dispersion equation (DE) describing waves in DR and GL.

    In this work, a development of the analytical and numerical methods [2, 3] are considered for the analysis of the electromagnetic wave propagation in metal-dielectric waveguides with multi-layered dielectric filling. The first step constitutes extension of the results obtained for symmetric complex waves in DR and GLto the case of non-symmetric (angle-dependent) waves, and the second step, to multi-layered dielectric covers. Both steps are accomplished using specific forms of DEs obtained in [3]by construction analytical continuation of the functions involved in DEs to multi-sheet Riemann surfaces of the spectral parameter and applying appropriate generalization the techniques [4]forfinding complex roots of the DEs.

    Calculation ofnon-symmetric complex waves employs numerical solution of the DEs with the help of parameter differentiation in the complex domain using multi-parameter setting and analysis of implicit functions of several complex variables [5] and reduction [2, 3] to numerical solution of auxiliary Cauchy problems.

    1. A. S. Raevskiiand S. B. Raevskii, Complex Waves, Radiotekhnika, Moscow, 2010.

    2. E. Kuzmina and Y. Shestopalov, “Waves in a lossyGoubau line,”10th European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland, 2016, doi: 10.1109/EuCAP.2016.7481368.

    3. E. Kuzmina and Y. Shestopalov, “Complex waves in a dielectric rod and Goubau line,” 19th Int. Conf. on Electromagneticsin Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 963-966, doi: 10.1109/ICEAA.2017.8065417.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

    5.Y. Shestopalov,“On unique solvability of multi-parameter waveguide inverse problems, ”19th Int. Conf. on Electromagnetics in Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 372-376, doi: 10.1109/ICEAA.2017.8065253.

  • 12.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Sheina, Elena
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Smirnov, Alexander
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems2018In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper (Refereed)
    Abstract [en]

    Development of the methods and algorithms [1, 2] are considered for the numerical solution to the forward problem of the electromagnetic wave scattering by inhomogeneous dielectric inclusions in a waveguide of rectangular cross section and inverse problem of reconstructing parameters of the dielectric inclusions from the values of the transmission coefficient of the scattered electromagnetic wave. The codes are developed implementing an FDTD method that employs the PML-layer technique. Numerical modeling and simulations are performed for the analysis of the wave propagation in waveguides of rectangular cross section loaded with parallel-plane layered media (layered dielectric diaphragms) and such diaphragms containing cubic dielectric inclusions. Validation is carried out of the results of calculations using closed-form solution [3] to the canonical single-layer structure.

    Progress in analytical - numerical investigations of the solutions to the forward and inverse waveguide problems are largely based on a recent discovery [4] of the singularities and extrema in the complex domain of the transmission coefficient of layered dielectric diaphragms. In fact, the knowledge of the location of singularity and extrema sets of the scattering matrix allows one to justify correct determination of real or complex permittivity of each layer of the diaphragm by specifying domains in the complex plane where the transmission coefficientis one-to-one; that is, the domains that do not contain singularities and where unique permittivity reconstruction is therefore possible. Forthe forward problem of the scattering of a normal waveguide mode by a single-and three-layer diaphragms with a dielectric cube, it is shown [1, 2] that variation in the values of the transmission coefficient can be up to two orders of magnitude less than that of the permittivity of the inclusion. Taking into account this result and the presence of singularities, improvements are proposed of the numerical method, algorithms and codes implementing the calculations. The results of modeling and computations are validated by comparing with experimental and measurement data [3]. The requirements are formulated that should be imposed on the accuracy of computations and measurements necessary to reconstruct numerically permittivity of the inclusion from the amplitude and phase of the transmitted wave with the prescribed accuracy.

    1. E. Sheina, A. Smirnov,Y. Shestopalov,and M.Ufimtsev,“FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy,”Progress in Electromagnetics Research Symposium (PIERS),St Petersburg, Russia, 2017, pp. 3188-3195, doi:10.1109/PIERS.2017.8262306.

    2.E. Sheina, A. Smirnov, and Y. Shestopalov, “Influence of standing waves on the solution of the inverse problem ofreconstructing parameters of a dielectric inclusion in a waveguide,”URSI Int. Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 2016,pp. 643-646, doi:10.1109/URSI-EMTS.2016.7571479.

    3. Yu. G. Smirnov, Yu. V. Shestopalov, and E. D. Derevyanchuk, “Inverse problem method for complex permittivity reconstruction of layered media in a rectangular waveguide,”Physica Status Solidi(C), 11,5-6, 2014,pp. 969–974, doi:10.1002/pssc.201300697.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

  • 13.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, Maxim
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.
    New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial2019In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper (Refereed)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 14.
    Smirnov, Yuri
    et al.
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line2019In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed)
    Abstract [en]

    The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

  • 15.
    Viirman, Olov
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Kristiansand, Norway.
    Nardi, Elena
    School of Education, University of East Anglia, Norwich, UK.
    Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modelling activities2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 2, p. 233-252Article in journal (Refereed)
    Abstract [en]

    Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

  • 16.
    Öberg, Karin
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Det behövs ett nytt verktyg för att reparera bristande baskunskaper i matematik: En studie om Elevate My Math´s effekter hos svensla gymnasieelever2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Mätningar av kunskaperna inom matematik hos svenska elever har under en längre tid visat på en nedåtgående trend. Samtidigt läser vi dagligen om den svenska lärarkårens höga arbetsbelastning. Syftet med det här examensarbetet är att undersöka en hållbar lösning, som både vänder den nedåtgående kunskapstrenden hos eleverna och dessutom underlättar lärarnas arbete. I Examensarbetet undersöks elevernas upplevelser samt kunskapsutveckling då de  arbetar med det digitala verktyget Elevate My Math.

    Undersökningen, som är både kvantitativ och kvalitativ görs i en ekonomiklass där halva klassen får arbeta med Elevate My Math och den andra halvan får jobba med ett material som vanligtvis används inom undervisningen. Resultaten visar att eleverna upplevelse av att arbeta med Elevate My Math är mycket positiv. Samtidigt visar resultatet att vidare forskning behövs för att säkerställa elevernas kunskapsutveckling vid användandet av Elevate My Math.

  • 17.
    Öhman, Johanna
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. 19881121-1542.
    Lärares syn och attityd på användandet av digitala verktyg inom matematikämnet2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
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